In this paper, we focus on the duo ring property via quasinilpotent elements, which gives a new kind of generalizations commutativity. We call rings qnil-duo. Firstly, some properties quasinilpotents in are provided. Then set is applied to rings, perspective, introduce and study right (resp., left) qnil-duo rings. show that concept not left-right symmetric. Among others, it proved if Hurwitz se...

Meta-projective modules on a ring R were essentially studied by Feng Lianggui and Tong Wenting in [3] when R is a commutative ring. While Duo-rings were studied by A. L. Fall in [2] and by M. Sanghare in [8]. The results of [3] were extended by M. O. Abdelkader in [5] to the duo-ring case by providing characterizations of Duo-rings. In this note, we give an extension of the MP-dimension notion ...